A Decision Logic Approach to Mill’s Eliminative Induction

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Abstract

The subject of the paper is a contemporary interpretation of J.S. Mill’s elimination method using selected concepts of Zdzisław Pawlak’s decision logic. The aim of the interpretation is to reformulate the original rules (canons) of Mill’s induction so that they correspond more precisely to his concept of cause as a complex sufficient condition. In the first part of the paper, we turn to Mill’s writings and justify the thesis that in his understanding the cause is an aggregation of circumstances, and not a single circumstance; next, we point out that Mill’s original canons (for example the canon of agreement and the canon of difference) do not allow causes-aggregations to be singled out from empirical data. In the second part of this paper, we present such aspects of Z. Pawlak’s decision logic that serve as the basis for the formalisation of the method of eliminative induction. We describe exhaustively the schema of induction that involves a gradual - divided into three stages - simplification of a set of implications corresponding to the observed dependencies [system of potential causes, effect]. The simplification is deductive because it maintains consistency within the set of implications. We show that such schema is ideal for isolating complex causes (aggregations of circumstances), ultimately described using complex conditional formulas of decision logic.

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